ALGEBRA 21 



3 . A/(*)-Ay(* + A)-Ay(*). 



= /(* + 3A) - 3/0 + aA) + 3/(* + A) -/(*). 



1.812 



1. A[c/0)].= cA/0) (c a constant). 



2. A[/iW + / 2 (*) + ....]- A/!(*) 



3. AC/i^./aW] =/i(*) A/ 2 (*) +/ 2 (a; + A)- A/i 



+ / 2 (*) 



1.813 The wth difference of a pol}momial of the nth degree is constant. If 

 f(x) = aoa; n + aix n ~ l + ..... + a^ix + a n 



1.82 



4 

 i. 



- i) (n - 2 ) (n-m + i)/? m 



_ b - ti) (x - b - 2/0 . . . .(x-b- n-m- iti). 



i 



2. A m 



* + 6) (x + 6 + A) (x + 6 + 2/0 . . . . (x + b + n-iti) 

 n ( + i) ( + 2) ( + m - 



+ h) (x + b+2ti) . . . . (x + b + n + m - lA) 

 3. A m a* = (a* - i) m a x 



4. 



5. A m sin (c* + (Q = f 2 sin 1 sin ( ex + d + m - 1 



6. A m cos (ex + d) = ( 2 sin J cos ( ex + d + m - J 



